Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in PYTHON3):

Solution:
import math
import sys
import collections
import bisect
import heapq



arr = list(map(int,sys.stdin.readline().strip().split()))
zeros = arr[0]
ones = arr[1]
k = arr[2]
pos = True

length = zeros + ones - 1
x = [1] + [0]*length
y = [1] + [0]*length

if k > length:
    print("No")
elif k == 0:
    print("Yes")
    st = '1'*ones + '0'*zeros
    print(st)
    print(st)
elif length == 1:
    print("No")
else:
    ix = 1
    iy = len(y)-1
    onesx = 1
    onesy = 1
    done = False
    
    y[iy] = 1
    onesy += 1
    curr = 1
    iy -= 1
    while onesy != ones:
        if iy <= 1:
            print("No")
            pos = False
            break
        if curr == k:
            x[iy] = 1
            onesx += 1
            iy -=1
            curr += 1
            done = True
        else:
            y[iy] = 1
            x[iy] = 1
            curr += 1
            onesy += 1
            onesx += 1
            iy -= 1

    #print(x)
    #print(y)
    #print(iy,curr)
    if pos:
        if not done:
            while curr < k:
                if iy <= 1:
                    print("No")
                    pos = False
                    break
                y[iy] = 0
                x[iy] = 0
                curr += 1
                iy -= 1

        if pos:
            if not done:
                x[iy] = 1
            print("Yes")
            for i in x:
                print(i, end="")
            print("")
            for i in y:
                print(i,end="")
            print("")